Effect of temperature on the mixed mode I/II translaminar fracture of laminated composites reinforced with natural fibers

Effect of temperature on the mixed mode I/II translaminar fracture of laminated composites reinforced with natural fibers | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Effect of temperature on the mixed mode I/II translaminar fracture of laminated composites reinforced with natural fibers Afshin Zeinedini, Yosra Basim Hassan This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4193231/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 14 Sep, 2024 Read the published version in Applied Composite Materials → Version 1 posted 9 You are reading this latest preprint version Abstract In recent years, laminated composites reinforced with natural fibers have extensively used in the various industries. One of the most important failure modes of laminated composite materials is translaminar fracture under different loading conditions. In this research, the effect of temperature on the translaminar critical strain energy release rate (CSERR) of the composites reinforced with cotton fibers was investigated. The cotton/epoxy samples were placed at different temperature conditions of 30, 0, and − 30°C. The translaminar CSERR values of cotton/epoxy laminated composites were obtained under pure mode I, mixed mode I/II with two different loading angles, and pure mode II loading conditions. To calculate the translaminar CSERR based on experimental results, numerical modeling was also performed. Besides, a modified version of Mixed Mode Fracture Envelope criterion was proposed to predict the mixed mode I/II translaminar fracture behavior of the cotton/epoxy laminated composites at the mentioned temperatures. The results showed that lowering the temperature has a great impact on the translaminar CSERR. It was also concluded that the change in the temperature had the greatest effect on the value of the mode I translaminar CSERR. Moreover, as the temperature decreased from 30 to 0 and − 30°C, the value of the mode I translaminar CSERR decreased around 80 and 90%, respectively. Epoxy fracture toughness natural fiber laminated composites temperature translaminar fracture Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 1. Introduction Laminated composite materials have been widely used due to their outstanding mechanical properties [ 1 ]. Natural laminated composites are those that their reinforcement, matrix or both of them are made of natural materials [ 2 ]. In recent years, these types of laminated composites have been increasingly applied due to their compatibility with the environment, low density, and economic efficiency [ 3 ]. In contrast, different types of damage modes may be occurred in these laminated composites [ 4 – 7 ]. Owing to the presence of fiber, three types of crack, i.e., interlaminar, intralaminar, and translaminar, may be occurred in the laminated composites [ 8 ]. Translaminar fracture has received less attention than the others [ 9 ]. This type of failure, like the others, may be caused under different loading conditions. Based on the direction of loading, mode I, mode II, and mode III translaminar fracture or any combination of them may occur in the laminated composites [ 10 ]. Most of researchers have studied the translaminar fracture behavior of laminated composites under mode I loading condition [ 11 – 16 ]. For example, Underwood and Kortschot [ 11 ], Gigliotti and Pinho [ 12 ] measured the translaminar fracture toughness (TFT) of the laminated composites reinforced by carbon fibers. Gonzalez et al. [ 13 ] explored the translaminar fracture behavior of laminated composites with the thermoplastic matrix and the woven carbon fibers reinforcement under tensile and compression loading conditions. The laminated composites were tested at room temperature and at 150°C, which is slightly higher than the glass transition temperature of the matrix. The results revealed that the translaminar fracture toughness increased slightly subjected to the tensile loading with the change of temperature, while under compressive loading, the temperature has a strong effect on the translaminar fracture toughness. In a study, Saadati et al. [ 14 ] studied the translaminar fracture behavior of flax/epoxy composite. These researchers obtained the mode I translaminar fracture toughness of flax/epoxy laminated composites under compressive and tensile loading states. The influence of matrix type on the translaminar fracture toughness of laminated composites was evaluated by Haldar et al. [ 15 ]. These researchers used unidirectional carbon fibers to reinforce the laminated composites. They observed that the type of matrix has a remarkable influence on the translaminar fracture toughness. Seyed Abdullah et al. [ 16 ] investigated the mode I translaminar fracture toughness of vectran/epoxy laminated composites. These researchers reported that under the mode I loading condition, the translaminar fracture toughness at the crack initiation of Vectran/epoxy laminated composites is relatively higher than the glass and carbon fiber reinforcement laminated composites. A few investigations have been carried out on the mixed mode I/II and mode II translaminmar fracture toughness of laminated composites reinforced by glass or carbon fibers [ 8 , 17 , 18 ]. For example, Desai et al. [ 17 ] experimentally investigated the mixed mode I/II translaminar fracture behavior of glass/epoxy laminated composites. The translaminar fracture test was performed on the samples at seven loading angles from 0 (pure mode I) to 90 degrees (pure mode II) with the step of 15 degrees. The results showed that the pure mode II critical strain energy release rate (CSERR) of glass/epoxy composites is higher than pure mode I CSERR. It was observed that under the mixed mode I/II loading condition, by increasing the contribution of mode II loading, the translaminar CSERR of glass/epoxy also increased. The effect of fiber type on the mode I, mixed mode I/II and mode II translaminar fracture toughness of laminated composites was studied by Taghibeigi et al. [ 8 ]. Carbon, Kevlar and glass fibers were considered as the reinforcement of laminated composites. The results manifested that the fiber type has a significant impact on the translaminar fracture toughness under different loading conditions. Zainaldini et al. [ 10 ] examined the translaminar fracture of modes I, II and III loading state and any combination of them of a cotton/epoxy laminated composites system. These researchers used a CTS sample to determine the translaminar CSERR of laminated composites reinforced by cotton fiber under a full range of loading conditions. The results declared that the translaminar CSERR of cotton/epoxy composites is remarkable compared to the artificial fiber/epoxy composites. Various environmental factors such as temperature, moisture, and impact caused by hailstone may affect the mechanical properties of laminated composites. To the best knowledge of the authors, the investigation of the mentioned factors on the translaminar fracture toughness of laminated composites reinforced by natural fibers has not yet been performed by the other researchers. Hence, the effect of temperature on the translaminar fracture toughness of laminated composites reinforced with natural fibers has been investigated in this work. Cotton fibers and an epoxy system were used as the reinforcement and the matrix, respectively. Three temperature conditions of 30, 0 and − 30 ˚ C were considered to achieve this purpose. The samples were tested under pure mode I, pure mode II, and mixed mode I/II loading conditions using an Arcan fixture. 2. Materials and methods 2.1. Materials Epoxies are the biggest category of thermoset polymers and have better mechanical properties than the other thermoset resins [ 19 ]. Epoxies are widely being used as the matrix of laminated composites by the researchers [ 20 – 24 ]. Ker828 epoxy resin and theta hardener (with a mixing ratio of 100:10) were used as the matrix system in this research. The density of the resin and the hardener are 1160 and 1130 kg/m3, respectively. It must be noted that resin system was supplied by Company KUMHO P&B Chemical Inc., Republic of Korea. In recent decades, different types of fibers have been used as reinforcement of laminated composite materials. Nowadays, natural fibers are extensively being applied to reinforce the polymer-based biocomposites due to their renewability, biocompatibility, low density and cost, and high specific mechanical properties. Natural fibers reinforced laminated composites have a remarkable role in the development of greener based materials [ 25 – 26 ]. In the current research, cotton fibers have been used as the reinforcement phase of the composite material. The woven natural cotton fibers used to reinforce the composites have a surface density of 171 g/m 2 . In order to characterize the cotton/epoxy laminated composites, ASTM D3039 [ 27 ] and ASTM D3518 [ 28 ] were used to obtain the mechanical properties under tensile and in-plane shear loading states. The samples were fabricated using the hand lay-up method. Six cotton/epoxy layers were used to manufacture the laminated composites plate. The tensile and in-plane shear samples were cut from the plate with the dimensions of 20×250 mm 2 according to ASTM D3039 [ 27 ] and ASTM D3518 [ 28 ]. The tensile and in-plane shear samples were tested using a universal testing machine (Santam STM-150) subjected to the displacement control quasi-static condition with a capacity of 150000 kg and loading rate of 1 mm/min (refer to Fig. 1 ). Mechanical properties of the laminated composites system and its constituents are listed in Table 1 . Table 1 The properties of epoxy, cotton fiber, and cotton/epoxy laminated composite systems The epoxy system (according to the supplier data sheet) E = 4.1 GPa, Ultimate tensile strength = 68 MPa, ρ (Density) = 1.16 g/cm 3 The cotton fiber [ 3 ] E = 5.5–6.12 GPa, Ultimate strength = 400 MPa, ρ (Density) = 1.5–1.6 g/cm 3 The cotton/epoxy laminated composites E 11 = E 22 = 4.82 GPa, v 12 = 0.21, G 12 = 2.74 GPa Ultimate tensile strength = 93.32 MPa, Fiber volume fraction = 23% 2.2. Samples and fixture manufacturing ASTM E1922 standard [ 29 ] is usually used to measure the mode I translaminar critical strain energy release rate. In this standard, a compact tension (CT) sample is considered to determine the mode I the translaminar CSERR of laminated composites. A modified version of the CT sample was also presented by Syed Abdullah et al. [ 16 ]. In the present study, the compact tension shear (CTS) proposed in Ref. [ 8 ] was used. Arcan fixture can be used to apply load on the CTS specimen. Figure 2 schematically displays the application of the Arcan fixture to apply pure mode I, pure mode II and mixed mode I/II loading on the CTS specimens. As observed, by testing the specimen under tensile loading, the mode I translaminar CSERR is computed. Besides, in order to calculate the mode II translaminar CSERR, the loading angle (α) must be equaled to 90˚. Furthermore, if the loading angle varies between 0 and 90˚, the mixed mode I/II translaminar CSERR can be measured. In Fig. 3 , the sample used and the Arcan fixture designed in this research have been displayed. It must be noted that Arcan fixture was made of Mo40 steel. It must be expressed that at least three samples were manufactured and tested to determine the translaminar fracture properties of the laminated composites under different loading conditions and temperature states. Hand lay-up method was used to fabricate the laminated composite panels. The panels were made of twelve layers of cotton/epoxy fibers with the stacking sequence of [0] 12 . Researchers have investigated the effect of sample thickness on the mode I translaminar CSERR of laminated composite materials [ 30 ]. It was concluded that the sample thickness does not have a significant effect on the translaminar CSERR of laminated composites. However, the low thickness of the specimen may cause out-of-plane buckling [ 29 ]. Therefore, in the present study, the thickness of CTS samples was considered to be 5 mm. The CTS samples with the dimensions of 60 mm × 37.5 mm were cut according to Fig. 3 . It should be noted that the other dimensions of the CTS specimens were selected based on Ref. [ 31 ]. The samples were cured for 24 hours at room temperature. Then the post-baking process was done by placing the samples in the oven for 4 hours at 85 ˚C. Furthermore, a sharp blade was applied to create a pre-crack at the tip of the samples. The pre-crack length was measured as 1 mm. To investigate the effect of temperature on the translaminar CSERR of laminated composites reinforced with cotton fibers, the samples were placed at temperatures of 30, 0 or -30 ˚C for one month. 3. Samples testing To perform the translaminar fracture test, the method proposed in ASTM E1922 standard was utilized [ 29 ]. In this method, the samples were loaded by the Arcan fixture at a speed of 1 mm/min. This test was performed using a universal testing machine (Santam STM-20) subjected to the displacement control quasi-static condition with a capacity of 2000 kg. In this test, the Arcan fixture was connected to the grips of the tensile test machine using the required parts and pins, and then the loading process was performed. Figure 4 shows the equipment required to carry out the fracture test. It must be mentioned that in addition to the pure mode I (α = 0º) and the pure mode II (α = 90º), two mixed mode I/II loading conditions with loading angles (α) of 30° and 60° were considered. Figure 5 displays the laminated composite samples under different loading conditions. 4. Numerical study Due to lack of the data reduction method to determine the translaminar CSERR of CTS samples, finite element analysis was usually used. The steps of calculating the translaminar CSERR have been reported by some researchers [ 8 – 10 ]. Based on these references, the CTS samples must be simulated with the Arcan fixture in a finite element-based software like Abaqus in the first step. As shown in Fig. 6 , a CTS specimen with a thickness of 1 mm was modeled. A certain load of 1 N was applied (P) to the CTS sample. Then, for each sample loaded under a certain loading condition, the compliance-crack length curve should be illustrated based on the modified compliance calibration (MCC) method. According to this method, to plot the compliance calibration curve, the CTS sample with different crack lengths must be simulated and analyzed. It should be noted that the contact between the CTS sample and the Arcan fixture was assumed to be frictionless. The laminated composites sample was fixed in the fixture by pins similar to the experimental method. In addition, the boundary conditions were considered on the basis of the experimental study. In total, 10,428 twenty-node reduced cubic elements (C3D20R) were used to mesh each CTS sample. The mesh sensitivity analysis was performed to obtain the optimum mesh size and the smallest element size around the crack tip was considered to be 0.1 mm. Finally, the determined compliance values were plotted versus the crack length. Based on the MCC method [ 8 – 10 ] and using the curve fitting method, a second-order polynomial equation was obtained for each compliance-crack length curve: $$C={\gamma a}^{2}+\delta a+{\lambda }$$ 1 where γ , δ and λ can be computed according to the curve fitting process. In addition, a is the crack length of the CTS sample. The translaminar CSERR of a laminated composites system under a specific loading condition can be computed by the following equation [ 8 – 10 ]: $${G}_{c}=\frac{{P}_{c}^{2}}{2t}\frac{dC}{da}$$ 2 where C , P c , and t are the compliance, the critical load, and the thickness of CTS sample. At the end, substituting Eq. ( 1 ) into Eq. ( 2 ), the translaminar CSERR of a laminated composites system can be determined as follows: $${G}_{c}={\left.\frac{{P}_{c}^{2}}{2t}(2\gamma a+\delta )\right|}_{a={a}_{0}}$$ 3 where a 0 is the summation of the pre-crack and notch lengths. Figure 7 shows the compliance-crack length plots obtained from the finite element analysis for the cotton/epoxy samples under different loadings. The translaminar CSERR components of the CTS specimen under any mixed mode I/II loading condition can be computed as follows: $${G}_{I}={\left.\frac{{\left({P}_{c}Cos\alpha \right)}^{2}}{2t}(2\gamma a+\delta )\right|}_{a={a}_{0}}$$ 4 $${G}_{II}={\left.\frac{{\left({P}_{c}Sin\alpha \right)}^{2}}{2t}(2\gamma a+\delta )\right|}_{a={a}_{0}}$$ 5 where \(\alpha\) is the loading angle as shown in Figs. 2 and 3 . It must be noted that \(\alpha =0\) and 90º denote the pure mode I and II loading conditions, respectively. In addition, under mixed mode I/II loading state, the total CSERR can be obtained as: $${G}_{c}={G}_{I}+{G}_{II}$$ 6 For the laminated composite materials under mode I and II loading states, the translaminar stress intensity factor can be written as a function of the strain energy release rate as follows [ 3 , 16 ]: $${K}_{I}=\sqrt{{G}_{I}{E}_{I}}$$ 7 $${K}_{II}=\sqrt{{G}_{II}{E}_{II}}$$ 8 In the above relations, E I and E II denote the effective tensile moduli of the laminated composites under a plane stress condition and can be determined by the following relations [ 3 ]: $${E}_{I}=\sqrt{2/\left({a}_{11}{a}_{22}\right)}/\sqrt{\sqrt{{a}_{22}/{a}_{11}}+\left\{\left({2a}_{12}+{a}_{66}\right)/\left({2a}_{11}\right)\right\}}$$ 9 $${E}_{II}=\left(\sqrt{2}/{a}_{11}\right)/\sqrt{\sqrt{{a}_{22}/{a}_{11}}+\left\{\left({2a}_{12}+{a}_{66}\right)/\left({2a}_{11}\right)\right\}}$$ 10 where a ij are written as functions of the engineering elastic terms of the laminated composites [ 3 ]: \({a}_{11}=\frac{1}{{E}_{xx}}\) , \({a}_{22}=\frac{1}{{E}_{yy}}\) , \({a}_{33}=\frac{1}{{E}_{zz}}\) , \({a}_{44}=\frac{1}{{G}_{yz}}\) , \({a}_{55}=\frac{1}{{G}_{xz}}\) , (11) \({a}_{66}=\frac{1}{{G}_{xy}}\) , \({a}_{12}={a}_{21}=-\frac{{\upsilon }_{xy}}{{E}_{xx}}=-\frac{{\upsilon }_{yx}}{{E}_{yy}}\) , \({a}_{13}={a}_{31}=-\frac{{\upsilon }_{xz}}{{E}_{xx}}=-\frac{{\upsilon }_{zx}}{{E}_{zz}}\) , \({a}_{23}={a}_{32}=-\frac{{\upsilon }_{yz}}{{E}_{yy}}=-\frac{{\upsilon }_{zy}}{{E}_{zz}}\) , In addition, the TFT of the laminate specimens subjected to any mixed mode loading state can be determined as follows: $${K}_{c}=\sqrt{{K}_{I}^{2}+{K}_{II}^{2}}$$ 12 5. Results and discussion 5.1. Load-displacement curves Typical load-displacement curves were obtained from the translaminar fracture testing of the cotton/epoxy samples under different temperature values and loading conditions. Figure 8 a shows the effect of mode mixity on the behavior of cotton/epoxy composites at 30 ˚C. As demonstrated, the area under the load-displacement curve is increased by enhancing the contribution of mode II loading condition. Figures 8 b and c display the response of the cotton/epoxy laminated composites having a translaminar crack under different loading conditions tested at 0 and − 30 ˚C, respectively. Figures 9 a-d demonstrate the influence of temperature on the load-displacement curves of translaminar fracture of cotton/epoxy samples under different loading states. As observed, the translaminar fracture behavior of the cotton/epoxy laminated composites is strongly influenced by temperature. It is well observed that under any loading condition, by decreasing the temperature, the maximum load and the maximum deflection of the cotton/epoxy sample is reduced significantly. Besides, when the cotton/epoxy laminated composites is placed at room temperature, the load-displacement of the CTS sample has a linear elastic behavior till the maximum load and then the load is reduced suddenly. However, by lowering the temperature from 30 to 0 ºC, in in addition to linear response, a non-linear behavior is observed in the load-displacement curve before the maximum load. For the samples placed at -30 ºC, a major non-linear behavior was observed before the maximum load. Besides, unlike the other curves, after the maximum load, the curve not only does not suddenly decrease but also slightly degrades. Three values for CSERR of a laminated composites system at the crack growth initiation state, i.e., onset of nonlinearity (NL), visual observation (VIS), and maximum load (MAX), have been introduced in the literature [ 4 , 33 ]. These values correspond to three values of load in the load-displacement curve of each fracture sample, i.e., P NL , P VIS , and P MAX . Some investigators [ 34 , 35 ] have expressed that the crack growth initiation occurs when P NL . The others have believed that the crack growth initiation in the laminated composites happens at P = P MAX [ 6 , 29 , 30 ]. Among the three CSERR initiation values, the NL CSERR ( G C - NL ) typically has the lowest value. Besides, according to ASTM E1922 [ 29 ], the upper bound value of the CSERR can be computed using the maximum load. Hence, in current research, the onset of nonlinearity load points were employed to compute the translaminar CSERR of the laminated composites under different loading and temperature conditions. In Table 2 , the values of critical load for cotton/epoxy samples exposed to different temperatures have been summarized. As mentioned, the samples were tested under pure mode I, pure mode II and mixed mode I/II loadings. The critical load is required to calculate the CSERR according to Eq. ( 3 ). Table 2 The critical load (N) values obtained for the cotton/epoxy laminated composites under different temperature and loading conditions Loading condition Temperature (˚C) 30 0 -30 Pure Mode I (α = 0º) 1131.8 ± 45.6 496.3 ± 18.9 150.3 ± 12.5 Mixed mode I/II (α = 30º) 1125.3 ± 37.8 816.9 ± 25.5 231.0 ± 10.7 Mixed mode I/II (α = 60º) 1270.4 ± 36.3 858.2 ± 23.8 297.9 ± 16.6 Pure Mode II (α = 90º) 1789.0 ± 65.7 1030.5 ± 38.1 450.6 ± 19.2 5.2. CSERR calculation The values of translaminar CSERR corresponded to the critical load ( P NL ) was determined using Eq. ( 3 ). According to the plots displayed in Fig. 7 , the translaminar critical strain energy release rate of cotton/epoxy samples under different temperature and loading conditions have been listed in Table 3 . As observed, by increasing the mode II loading contribution, the value of the translaminar CSERR increases. In other words, the lowest and highest values of the translaminar CSERR are obtained when the samples are tested under the pure modes I and II, respectively. In addition, as the temperature decreases, the values of the CSERR degrade significantly. The biggest reduction was also calculated for the sample tested under the mode I loading state. Gonzalez et al. [ 13 ] observed that the translaminar fracture toughness of a thermoplastic laminated composites is increased slightly subjected to the tensile loading with the change of temperature from 0 to 150 ºC, while under compressive loading, the temperature has a strong effect on the translaminar fracture toughness. Table 3 The translaminar critical strain energy release rate (kJ/m 2 ) of the cotton/epoxy laminated composites under different temperature values and loading conditions Loading condition Temperature (˚C) 30 0 -30 Pure Mode I (α = 0º) 10.37 ± 0.85 1.99 ± 0.15 0.19 ± 0.03 Mixed mode I/II (α = 30º) 11.76 ± 0.80 6.19 ± 0.39 0.49 ± 0.05 Mixed mode I/II (α = 60º) 11.92 ± 0.69 5.44 ± 0.30 0.66 ± 0.08 Pure Mode II (α = 90º) 12.32 ± 0.92 4.09 ± 0.31 0.78 ± 0.07 5.3. Fracture envelops In literature, different criteria have been proposed to investigate the response of the laminated composites system under mixed mode I/II loading conditions. Mixed Mode Fracture Envelope (MMFE) is extensively employed to evaluate the fracture testing of laminated composites [ 31 ]. In this study, a modified MMFE is proposed to estimate the mixed mode I/II translaminar behavior of the cotton/epoxy laminated composites at different temperatures. This criterion is expressed by the following relation: $$\frac{{(\frac{{K}_{I}}{{K}_{IC}}-m)}^{2}}{{X}^{2}}+\frac{{(\frac{{K}_{II}}{{K}_{IIC}}-n)}^{2}}{{Y}^{2}}=1$$ 13 Figures 10 a-b show the mixed mode I/II translaminar fracture envelope for the cotton/epoxy laminated composites at 30, 0, and − 30 ºC. It was concluded that the form of m = n = 0 and X = Y = 1 is properly predicted the translaminar fracture response of the cotton/epoxy laminated composites at 30 ºC (see Fig. 10 a). These fitted Modified MMFE relations for the system at 0 and − 30 ºC have also been shown in Figs. 10 b-c. As observed, the modified MMFE is able to predict the mixed mode I/II translaminar fracture response of the cotton/epoxy laminated composites at different temperature conditions. 6. Conclusions In the present research, the effect of temperatures on the translaminar fracture properties of the cotton/epoxy laminated composites under pure mode I, pure mode II and mixed mode I/II loading conditions was investigated. Some achievements of this research have been summarized as follows: Temperature greatly affects the translaminar fracture properties of cotton/epoxy composites. The results showed that temperature has the greatest effect on the mode I CSERR. As the temperature decreased from 30 to 0°C, the translaminar CSERR under mode I loading condition degraded by 80%. In addition, the temperature decreased from 0 to -30°C, the mode I translaminar CSERR decreased around 90%. Among the different loading states, the mode II had the least dependence on the temperature. As the temperature decreased from 30 to 0°C, the value of the mode II translaminar CSERR decreased by 66%. By changing the loading condition from the mode I to the mixed mode I/II as well as the mode II, the amount of translaminar CSERR decreased. In other words, with the enhancement of the contribution of the mode II loading condition, the value of the translaminar CSERR increased. A modified version of Mixed Mode Fracture Envelope criterion was proposed to predict the translaminar fracture response of the cotton/epoxy laminated composites placed at different temperature values under mixed mode I/II loading conditions. Nomenclature a 0 Summation of pre-crack and notch lengths n Fracture envelop parameter P Applied load a Notch length P C Critical applied load C Compliance W CTS sample width E I & E II Effective tensile stiffnesses t CTS sample thickness E xx Longitudinal tensile stiffness X Fracture envelop parameter E yy Transverse tensile stiffness Y Fracture envelop parameter E s In-plane shear stiffness Abbreviations G Strain energy release rate ASTM American Society for Testing and Materials G c Critical strain energy release rate (CSERR) C3D20R Reduced twenty-node quadratic elements CSERR critical strain energy release rate G Ic Mode I CSERR CT Compact Tension G IIc Mode II CSERR CTS Compact Tension Shear G I-IIc Mixed mode I/II CSERR FEM Finite Element method H CTS sample height MCC Modified Compliance Calibration K I Mode I stress intensity factor (SIF) NL Onset of non-linearity TFT Translaminar Fracture Toughness K II Mode II SIF VIS Visual observation K Ic Mode I translaminar fracture toughness (TFT) Greek letters K IIc Mode II TFT α In-plane loading angle K I-IIc Mixed mode I/II TFT v Poisson’s ratio K T Total SIF γ Compliance fitting parameter m Fracture envelop parameter δ Compliance fitting parameter Declarations Ethical Approval The authors certify that they have NO affiliations with or involvement in any organization or entity with any financial interest, or non-financial interest in the subject matter or materials discussed in this work. Funding This research received no grant from any funding agency in the public, commercial, or the others. Author Contribution Afshin Zeinedini wrote the main manuscript, prepared the figures, and carried out the FE analysis. Yosra Basim Hassan performed the experimental study. Availability of data and materials The raw/processed data required to reproduce these findings cannot be shared at this time as the data also forms part of an ongoing study. References Zeinedini, A., Hosseini, Y., Mahdi, A.S. et al.: Impact of the Manufacturing Process on the Flexural Properties of Laminated Composite-Metal Riveted Joints: Experimental and Numerical Studies. Appl. Compos. Mater. 31 (2024) 583–610. https://doi.org/10.1007/s10443-023-10186-w Cai, M., Liu, J., Zhang, X. et al.: Mechanical Stability of Carbon/Ramie Fiber Hybrid Composites Under Hygrothermal Aging. 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(2018). https://doi.org/10.1016/j.tafmec.2018.06.002 Zeinedini, A., Shokrieh, M.M., Ebrahimi, A.: The effect of agglomeration on the fracture toughness of CNTs-reinforced nanocomposites. Theor. Appl. Fract. Mech. (2018). https://doi.org/10.1016/j.tafmec.2018.01.009 Taghibeigi, H., Zeinedini, A., Oleiwi, A.H.: On the mixed mode I/II translaminar fracture of plain-weave carbon, E-glass and Kevlar reinforced laminated composites. Compos. Sci. Tech. (2023). https://doi.org/10.1016/j.compscitech.2023.110117 Laffan, M.J., Pinho, S.T., Robinson, P., McMillan, A.J.: Translaminar fracture toughness testing of composites: a review. Polym. Test. (2012). https://doi.org/10.1016/j.polymertesting.2012.01.002 Zeinedini, A., Moradi, M.H., Taghibeigi, H., Jamali, J.: on the mixed mode I/II/III translaminar fracture thoughness of Cotton/epoxy laminated composites. Theor. Appl. Fract. Mech. (2020). https://doi.org/10.1016/j.tafmec.2020.102760 Underwood, J.H., Kortschot, M.T.: Notch-tip Damage and Translaminar Fracture Toughness Measurements from Carbon/Epoxy Laminates. US Army Armament Research. Development and Engineering Centre, Technical Report ARCCB-TR-94010 (1994). Gigliotti, L., Pinho, S.T.: Translaminar fracture toughness of NCF composites with multiaxial blankets. Mater. Des. (2016). https://doi.org/10.1016/j.matdes.2015.12.167 Gonzalez, J.D.P., Vieille, B., Bouvet, C.: High temperature translaminar fracture of Woven-ply thermoplastic laminates in tension and in compression. Eng. Fract. Mech. (2021). https://doi.org/10.1016/j.engfracmech.2021.107616 Saadati, Y., Lebrun, G., Bouvet, C., Chatelain, J.F.: Study of translaminar Fracture Thoughness of unidirectional Flax/epoxy composite. Compos. C: Open Access (2020). https://doi.org/10.1016/j.jcomc.2020.100008 Haldar, S . , Herraez, M., Naya, F., Gonzalez, C., Lopes, S.C.: Relations between interlaminar micromechanisms and translaminar fracture behavior of unidirectional FRP supported by experimental mocromechanics. Compos. B Eng. (2019). https://doi.org/10.1016/j.compositesb.2019.107000 Syed Abdullah, S.I.B., Iannucci L., Greenhalgh E.S.: On the translaminar fracture thoughness of vectran/epoxy composite material. Compos. Struct. (2018). https://doi.org/10.1016/j.compstruct.2018.03.004 Desai, A., Sharanaprabhu, C.M., Kudari, S.K.: Study on translaminar fracture Toughness under mixed mode I/II load for (0/45) orientation unidirectional glass/epoxy composite. Mater. Today Proc. (2021). https://doi.org/10.1016/j.matpr.2020.08.206 Laffan, M.J., Pinho, S.T., Robinson, P.: Mixed-mode translaminar fracture of CFRP: Failure analysis and fractography. Compos. Struct. (2013). https://doi.org/10.1016/j.compstruct.2012.06.012 Moradi, E., Zeinedini, A., Heidari Shahmaleki, E.: Mechanical properties of laminated composites reinforced by natural fibers of cotton, wool and kenaf under tensile, flexural and shear loadings. J.ournal of Science and Technology of Composites (2019). Shahbazi, A., Zeinedini, A.: Impact Response of E-glass/epoxy Composite Bi-directional Corrugated Core Sandwich Panels. Polym. Polym. Compos. (2020). https://doi.org/10.1177/0967391120982751 Doostvandi, B., Zeinedini, A.: Repair of inclined notches in the pressurized steel pipes using laminated composites, Material Design & Processing Communications, Mat Design Process Comm (2019). https://doi.org/10.1002/mdp2.49 Shahmaleki, M., Zeinedini, A.: Flexural Properties of 3D-printed Hierarchical-Sinusoidal Corrugated Core Sandwich Panels with Natural Fiber Reinforced Skins. Polym. Polym. Compos. (2022). https://doi.org/10.1177/09673911221101299 Daliri, V., Zeinedini, A.: Flexural Behavoiur of the Composite Sandwich Panels with Novel and Regular Corrugated Cores. Appl Compos Mater (2019). https://doi.org/10.1007/s10443-019-09761-x Piroozfar, S., Zeinedini, A.: Effect of Geometrical Parameters on the Flexural Properties of Sandwich Structures with 3D-printed Honeycomb Core and E-glass/epoxy Face-sheets. Struct. (2021). https://doi.org/10.1016/j.istruc.2021.06.033 Pickering, K.L., Aruan Efendy, M.G., Le, T.M.: A review of recent developments in natural fibre composites and their mechanical performance. Compos. - A: Appl. Sci. Manuf. (2016). https://doi.org/10.1016/j.compositesa.2015.08.038 Karimah, A., Ridho, M.R., Munawar S.S., Adi D.S., Ismadi, Damayanti. R., Subiyanto, B., Fatriasari, W., Fudholi, A.: A review on natural fibers for development of eco-friendly bio-composite: characteristics, and utilizations. J. Mater. Res. Technol. (2021). https://doi.org/10.1016/j.jmrt.2021.06.014. ASTM D3039/D3039M-08.: Standard test method for tensile properties of polymer matrix composite materials. ASTM International, Philadelphia (2014). ASTM D3518/D3518M-18.: Standard Test Method for In-Plane Shear Response of Polymer Matrix Composite Materials by Tensile Test of a ±45 Laminate. ASTM International, Philadelphia (2018). ASTM E1922.: Standard Test Method for Translaminar Fracture Toughness of Laminated and Pultruded Polymer Matrix Composite Materials. ASTM International, Philadelphia (2015). Teixeira, R.F., Pinho, S.T., Robinson, P.: Thickness-dependence of the translaminar fracture toughness: experimental study using thin-ply composites. Compos. Part A Appl. Sci. Manuf. (2016). https://doi.org/10.1016/j.compositesa.2016.05.031 Zeinedini, A.: A novel fixture for mixed mode I/II/III fracture testing of brittle materials. Fatigue Fract Eng Mater Struct. (2018). https://doi.org/10.1111/ffe.12955 Swolfs, Y., Geboes, Y., Gorbatikh, L., Pinho, S.T.: The importance of translaminar fracture toughness for the penetration impact behavior of woven carbon/glass hybrid composites. Compos. Appl. Sci. Manuf. (2017). https://doi.org/10.1016/j.compositesa.2017.09.009 ASTM D5528.: Standard Test Method for Mode I Interlaminar Fracture Toughness of Unidirectional Fiber-Reinforced Polymer Matrix Composites. ASTM International, Philadelphia (2013). El-Sagheer, I., Abd-Elhady, A.A., Sallam, H.M., Naga, S.A.R.: An Assessment of ASTM E1922 for Measuring the Translaminar Fracture Toughness of Laminated Polymer Matrix Composite Materials. Polymers (2021). https://doi.org/10.3390/polym13183129 Ozdemir, A.O., Karata, C.: Experimental determination of fracture toughness of woven/chopped glass fiber hybrid reinforced thermoplastic composite laminates. Sci. Iran. B (2021). https://doi.org/10.24200/SCI.2020.56380.4701 Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 14 Sep, 2024 Read the published version in Applied Composite Materials → Version 1 posted Editorial decision: Revision requested 30 May, 2024 Reviews received at journal 30 May, 2024 Reviewers agreed at journal 09 May, 2024 Reviews received at journal 16 Apr, 2024 Reviewers agreed at journal 11 Apr, 2024 Reviewers invited by journal 09 Apr, 2024 Editor assigned by journal 03 Apr, 2024 Submission checks completed at journal 01 Apr, 2024 First submitted to journal 30 Mar, 2024 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4193231","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":286960590,"identity":"beba8d21-9994-434a-91c3-556caa0c14f2","order_by":0,"name":"Afshin Zeinedini","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAzklEQVRIiWNgGAWjYFACxgYGBjYJBjb2NqgAM9FaeI4xMBwgTgsIsAGxRBpUCyEg397c9uBDmUUen+SzNOkPDHbyDOy8D/A7q+dgu+GMcxLFbNJpxyQOMCQbNjCzG+DVwiyR2CbN2wYi09uAWpgTGJjZCPhC/mGb9F+QFsnjIC31hLXwSDC2STOCtEiwgRx2mLAWCR6g+T3ngFp40pItzhgcN2wjpEW+/fgziR9ldYnz248Z3qioqJbn5z+GXwsaMIDE0SgYBaNgFIwCCgEATeY3ZJoV7L4AAAAASUVORK5CYII=","orcid":"","institution":"Kermanshah University of Technology","correspondingAuthor":true,"prefix":"","firstName":"Afshin","middleName":"","lastName":"Zeinedini","suffix":""},{"id":286960591,"identity":"35adafdb-1199-4b6e-b8ea-0eddcd60ba64","order_by":1,"name":"Yosra Basim Hassan","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Yosra","middleName":"Basim","lastName":"Hassan","suffix":""}],"badges":[],"createdAt":"2024-03-30 18:12:23","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4193231/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4193231/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s10443-024-10267-4","type":"published","date":"2024-09-14T15:57:28+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":54102274,"identity":"263ff242-e4af-4037-b1a0-423251cdee78","added_by":"auto","created_at":"2024-04-04 16:01:20","extension":"jpg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":63417,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eThe experiment setup used to characterize mechanical properties of the cotton/epoxy and the pure epoxy under tensile and in-plane shear loading conditions. The tested cotton/epoxy sample under tensile loading state has been displayed.\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"1.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4193231/v1/e7fb2fb50f0c8c0ea97714e5.jpg"},{"id":54102272,"identity":"72661cc5-36e0-4acb-8663-3a446dc25b43","added_by":"auto","created_at":"2024-04-04 16:01:20","extension":"jpg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":36351,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eThe application of the Arcan fixture to apply pure mode I, pure mode II and mixed mode I/II loading on the CTS sample\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"2.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4193231/v1/9161e13c8d53e32577d5f690.jpg"},{"id":54102275,"identity":"b4680473-6393-4f35-b94a-dc222aab2371","added_by":"auto","created_at":"2024-04-04 16:01:20","extension":"jpg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":31910,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eThe dimensions of CTS sample and the Arcan fixture used in the current research\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"3.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4193231/v1/ec224ecfa1731631ccffa842.jpg"},{"id":54102279,"identity":"ed498ec1-b33e-4da1-a7ce-45f398806c27","added_by":"auto","created_at":"2024-04-04 16:01:20","extension":"jpg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":51981,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eThe requirement setup for translaminar fracture test\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"4.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4193231/v1/c15ba21689c52fc564d5c5a9.jpg"},{"id":54102276,"identity":"6962212a-ea71-41bd-9d81-37ea7e6a9a5b","added_by":"auto","created_at":"2024-04-04 16:01:20","extension":"jpg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":44630,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eThe images of samples under (a) the pure mode I, (b) the mixed mode I/II with the loading angle of 30º, (c) the mixed mode I/II with the loading angle of 60º, and (d) the pure mode II loading conditions\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"5.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4193231/v1/bae85cf17bc46a8d869c1f7d.jpg"},{"id":54102273,"identity":"0ef1fa08-3f5f-423c-a0e5-333cc8238bc8","added_by":"auto","created_at":"2024-04-04 16:01:20","extension":"jpg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":100431,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eThe CTS specimen with the Arcan fixture simulated in Abaqus and the detail of the pre-crack tip area\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"6.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4193231/v1/a231ce1ab86dcaed35116fd4.jpg"},{"id":54102278,"identity":"d0c76923-37c5-4259-8fd9-6ffe74637b7d","added_by":"auto","created_at":"2024-04-04 16:01:20","extension":"jpg","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":68785,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eThe compliance-crack length curves obtained from the finite element analysis for the cotton/epoxy under (a) mode I, (b) mode II, (c) mixed mode I/II with loading angle of 30º, and (d) mixed mode I/II with loading angle of 60ºloading conditions\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"7.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4193231/v1/931830c341c2d32561d0d219.jpg"},{"id":54102283,"identity":"b6cc2ba3-4f94-4bd3-ad3d-430fe9966ef3","added_by":"auto","created_at":"2024-04-04 16:01:20","extension":"jpg","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":215292,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eTypical load-displacement curves of the cotton/epoxy system consisting of a translaminar crack tested at (a) 30 ºC, (b) 0 ºC, and (c) -30 ºC under different loading conditions\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"8.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4193231/v1/b99cc6b77ff6c056dcf58a3c.jpg"},{"id":54102281,"identity":"207fc079-a2a2-46d5-8a6f-1312491e4a3d","added_by":"auto","created_at":"2024-04-04 16:01:20","extension":"jpg","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":64948,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eEffect of temperature on the load-displacement curves of the cotton/epoxy laminates under (a) mode I, (b) mode II, (c) mixed mode I/II with loading angles of 30º and (d) mixed mode I/II with loading angles of 60º loading conditions\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"9.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4193231/v1/2dc9cf497ac8aaf137e9deb1.jpg"},{"id":54102754,"identity":"a4dc4150-5fd6-4826-bf90-a16950ba456b","added_by":"auto","created_at":"2024-04-04 16:09:20","extension":"jpg","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":199764,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eThe mixed mode I/II translaminar fracture envelopes for the cotton/epoxy laminated composites placed at (a) 30, (b) 0, (c) and -30 ºC.\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"10.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4193231/v1/a1c1a0cac86e1b977ba03389.jpg"},{"id":64619073,"identity":"c00fee34-b499-4f31-ac66-1a1664dcd601","added_by":"auto","created_at":"2024-09-16 16:11:10","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1841017,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4193231/v1/52aeaa68-15d0-4227-971d-b4cdac5c7672.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Effect of temperature on the mixed mode I/II translaminar fracture of laminated composites reinforced with natural fibers","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eLaminated composite materials have been widely used due to their outstanding mechanical properties [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. Natural laminated composites are those that their reinforcement, matrix or both of them are made of natural materials [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]. In recent years, these types of laminated composites have been increasingly applied due to their compatibility with the environment, low density, and economic efficiency [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. In contrast, different types of damage modes may be occurred in these laminated composites [\u003cspan additionalcitationids=\"CR5 CR6\" citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]. Owing to the presence of fiber, three types of crack, i.e., interlaminar, intralaminar, and translaminar, may be occurred in the laminated composites [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. Translaminar fracture has received less attention than the others [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]. This type of failure, like the others, may be caused under different loading conditions. Based on the direction of loading, mode I, mode II, and mode III translaminar fracture or any combination of them may occur in the laminated composites [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]. Most of researchers have studied the translaminar fracture behavior of laminated composites under mode I loading condition [\u003cspan additionalcitationids=\"CR12 CR13 CR14 CR15\" citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]. For example, Underwood and Kortschot [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e], Gigliotti and Pinho [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e] measured the translaminar fracture toughness (TFT) of the laminated composites reinforced by carbon fibers. Gonzalez et al. [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e] explored the translaminar fracture behavior of laminated composites with the thermoplastic matrix and the woven carbon fibers reinforcement under tensile and compression loading conditions. The laminated composites were tested at room temperature and at 150\u0026deg;C, which is slightly higher than the glass transition temperature of the matrix. The results revealed that the translaminar fracture toughness increased slightly subjected to the tensile loading with the change of temperature, while under compressive loading, the temperature has a strong effect on the translaminar fracture toughness. In a study, Saadati et al. [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e] studied the translaminar fracture behavior of flax/epoxy composite. These researchers obtained the mode I translaminar fracture toughness of flax/epoxy laminated composites under compressive and tensile loading states. The influence of matrix type on the translaminar fracture toughness of laminated composites was evaluated by Haldar et al. [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]. These researchers used unidirectional carbon fibers to reinforce the laminated composites. They observed that the type of matrix has a remarkable influence on the translaminar fracture toughness. Seyed Abdullah et al. [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e] investigated the mode I translaminar fracture toughness of vectran/epoxy laminated composites. These researchers reported that under the mode I loading condition, the translaminar fracture toughness at the crack initiation of Vectran/epoxy laminated composites is relatively higher than the glass and carbon fiber reinforcement laminated composites.\u003c/p\u003e \u003cp\u003eA few investigations have been carried out on the mixed mode I/II and mode II translaminmar fracture toughness of laminated composites reinforced by glass or carbon fibers [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e, \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e, \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]. For example, Desai et al. [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e] experimentally investigated the mixed mode I/II translaminar fracture behavior of glass/epoxy laminated composites. The translaminar fracture test was performed on the samples at seven loading angles from 0 (pure mode I) to 90 degrees (pure mode II) with the step of 15 degrees. The results showed that the pure mode II critical strain energy release rate (CSERR) of glass/epoxy composites is higher than pure mode I CSERR. It was observed that under the mixed mode I/II loading condition, by increasing the contribution of mode II loading, the translaminar CSERR of glass/epoxy also increased. The effect of fiber type on the mode I, mixed mode I/II and mode II translaminar fracture toughness of laminated composites was studied by Taghibeigi et al. [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. Carbon, Kevlar and glass fibers were considered as the reinforcement of laminated composites. The results manifested that the fiber type has a significant impact on the translaminar fracture toughness under different loading conditions. Zainaldini et al. [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e] examined the translaminar fracture of modes I, II and III loading state and any combination of them of a cotton/epoxy laminated composites system. These researchers used a CTS sample to determine the translaminar CSERR of laminated composites reinforced by cotton fiber under a full range of loading conditions. The results declared that the translaminar CSERR of cotton/epoxy composites is remarkable compared to the artificial fiber/epoxy composites.\u003c/p\u003e \u003cp\u003eVarious environmental factors such as temperature, moisture, and impact caused by hailstone may affect the mechanical properties of laminated composites. To the best knowledge of the authors, the investigation of the mentioned factors on the translaminar fracture toughness of laminated composites reinforced by natural fibers has not yet been performed by the other researchers. Hence, the effect of temperature on the translaminar fracture toughness of laminated composites reinforced with natural fibers has been investigated in this work. Cotton fibers and an epoxy system were used as the reinforcement and the matrix, respectively. Three temperature conditions of 30, 0 and \u0026minus;\u0026thinsp;30 \u003csup\u003e˚\u003c/sup\u003eC were considered to achieve this purpose. The samples were tested under pure mode I, pure mode II, and mixed mode I/II loading conditions using an Arcan fixture.\u003c/p\u003e"},{"header":"2. Materials and methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1. Materials\u003c/h2\u003e \u003cp\u003eEpoxies are the biggest category of thermoset polymers and have better mechanical properties than the other thermoset resins [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]. Epoxies are widely being used as the matrix of laminated composites by the researchers [\u003cspan additionalcitationids=\"CR21 CR22 CR23\" citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e]. Ker828 epoxy resin and theta hardener (with a mixing ratio of 100:10) were used as the matrix system in this research. The density of the resin and the hardener are 1160 and 1130 kg/m3, respectively. It must be noted that resin system was supplied by Company KUMHO P\u0026amp;B Chemical Inc., Republic of Korea.\u003c/p\u003e \u003cp\u003eIn recent decades, different types of fibers have been used as reinforcement of laminated composite materials. Nowadays, natural fibers are extensively being applied to reinforce the polymer-based biocomposites due to their renewability, biocompatibility, low density and cost, and high specific mechanical properties. Natural fibers reinforced laminated composites have a remarkable role in the development of greener based materials [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e]. In the current research, cotton fibers have been used as the reinforcement phase of the composite material. The woven natural cotton fibers used to reinforce the composites have a surface density of 171 g/m\u003csup\u003e2\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eIn order to characterize the cotton/epoxy laminated composites, ASTM D3039 [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e] and ASTM D3518 [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e] were used to obtain the mechanical properties under tensile and in-plane shear loading states. The samples were fabricated using the hand lay-up method. Six cotton/epoxy layers were used to manufacture the laminated composites plate. The tensile and in-plane shear samples were cut from the plate with the dimensions of 20\u0026times;250 mm\u003csup\u003e2\u003c/sup\u003e according to ASTM D3039 [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e] and ASTM D3518 [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e]. The tensile and in-plane shear samples were tested using a universal testing machine (Santam STM-150) subjected to the displacement control quasi-static condition with a capacity of 150000 kg and loading rate of 1 mm/min (refer to Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). Mechanical properties of the laminated composites system and its constituents are listed in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eThe properties of epoxy, cotton fiber, and cotton/epoxy laminated composite systems\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"1\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eThe epoxy system (according to the supplier data sheet)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eE\u0026thinsp;=\u003c/em\u003e\u0026thinsp;4.1 GPa, Ultimate tensile strength\u0026thinsp;=\u0026thinsp;68 MPa, \u003cem\u003eρ\u003c/em\u003e (Density)\u0026thinsp;\u003cem\u003e=\u003c/em\u003e\u0026thinsp;1.16 g/cm\u003csup\u003e3\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eThe cotton fiber\u003c/b\u003e [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eE\u0026thinsp;=\u003c/em\u003e\u0026thinsp;5.5\u0026ndash;6.12 GPa, Ultimate strength\u0026thinsp;=\u0026thinsp;400 MPa, \u003cem\u003eρ\u003c/em\u003e (Density)\u0026thinsp;\u003cem\u003e=\u003c/em\u003e\u0026thinsp;1.5\u0026ndash;1.6 g/cm\u003csup\u003e3\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eThe cotton/epoxy laminated composites\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eE\u003c/em\u003e\u003csub\u003e11\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;\u003cem\u003eE\u003c/em\u003e\u003csub\u003e22\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;4.82 GPa, \u003cem\u003ev\u003c/em\u003e\u003csub\u003e12\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.21, \u003cem\u003eG\u003c/em\u003e\u003csub\u003e12\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;2.74 GPa\u003c/p\u003e \u003cp\u003eUltimate tensile strength\u0026thinsp;=\u0026thinsp;93.32 MPa, Fiber volume fraction\u0026thinsp;=\u0026thinsp;23%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2. Samples and fixture manufacturing\u003c/h2\u003e \u003cp\u003eASTM E1922 standard [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e] is usually used to measure the mode I translaminar critical strain energy release rate. In this standard, a compact tension (CT) sample is considered to determine the mode I the translaminar CSERR of laminated composites. A modified version of the CT sample was also presented by Syed Abdullah et al. [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]. In the present study, the compact tension shear (CTS) proposed in Ref. [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e] was used. Arcan fixture can be used to apply load on the CTS specimen. Figure\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e schematically displays the application of the Arcan fixture to apply pure mode I, pure mode II and mixed mode I/II loading on the CTS specimens. As observed, by testing the specimen under tensile loading, the mode I translaminar CSERR is computed. Besides, in order to calculate the mode II translaminar CSERR, the loading angle (α) must be equaled to 90˚. Furthermore, if the loading angle varies between 0 and 90˚, the mixed mode I/II translaminar CSERR can be measured.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIn Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e, the sample used and the Arcan fixture designed in this research have been displayed. It must be noted that Arcan fixture was made of Mo40 steel. It must be expressed that at least three samples were manufactured and tested to determine the translaminar fracture properties of the laminated composites under different loading conditions and temperature states.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eHand lay-up method was used to fabricate the laminated composite panels. The panels were made of twelve layers of cotton/epoxy fibers with the stacking sequence of [0]\u003csub\u003e12\u003c/sub\u003e. Researchers have investigated the effect of sample thickness on the mode I translaminar CSERR of laminated composite materials [\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e]. It was concluded that the sample thickness does not have a significant effect on the translaminar CSERR of laminated composites. However, the low thickness of the specimen may cause out-of-plane buckling [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e]. Therefore, in the present study, the thickness of CTS samples was considered to be 5 mm. The CTS samples with the dimensions of 60 mm \u0026times; 37.5 mm were cut according to Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. It should be noted that the other dimensions of the CTS specimens were selected based on Ref. [\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e]. The samples were cured for 24 hours at room temperature. Then the post-baking process was done by placing the samples in the oven for 4 hours at 85 ˚C. Furthermore, a sharp blade was applied to create a pre-crack at the tip of the samples. The pre-crack length was measured as 1 mm. To investigate the effect of temperature on the translaminar CSERR of laminated composites reinforced with cotton fibers, the samples were placed at temperatures of 30, 0 or -30 ˚C for one month.\u003c/p\u003e \u003c/div\u003e"},{"header":"3. Samples testing","content":"\u003cp\u003eTo perform the translaminar fracture test, the method proposed in ASTM E1922 standard was utilized [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e]. In this method, the samples were loaded by the Arcan fixture at a speed of 1 mm/min. This test was performed using a universal testing machine (Santam STM-20) subjected to the displacement control quasi-static condition with a capacity of 2000 kg. In this test, the Arcan fixture was connected to the grips of the tensile test machine using the required parts and pins, and then the loading process was performed. Figure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e shows the equipment required to carry out the fracture test.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIt must be mentioned that in addition to the pure mode I (α\u0026thinsp;=\u0026thinsp;0\u0026ordm;) and the pure mode II (α\u0026thinsp;=\u0026thinsp;90\u0026ordm;), two mixed mode I/II loading conditions with loading angles (α) of 30\u0026deg; and 60\u0026deg; were considered. Figure\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e displays the laminated composite samples under different loading conditions.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"4. Numerical study","content":"\u003cp\u003eDue to lack of the data reduction method to determine the translaminar CSERR of CTS samples, finite element analysis was usually used. The steps of calculating the translaminar CSERR have been reported by some researchers [\u003cspan additionalcitationids=\"CR9\" citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]. Based on these references, the CTS samples must be simulated with the Arcan fixture in a finite element-based software like Abaqus in the first step. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e, a CTS specimen with a thickness of 1 mm was modeled. A certain load of 1 N was applied (P) to the CTS sample. Then, for each sample loaded under a certain loading condition, the compliance-crack length curve should be illustrated based on the modified compliance calibration (MCC) method. According to this method, to plot the compliance calibration curve, the CTS sample with different crack lengths must be simulated and analyzed. It should be noted that the contact between the CTS sample and the Arcan fixture was assumed to be frictionless. The laminated composites sample was fixed in the fixture by pins similar to the experimental method. In addition, the boundary conditions were considered on the basis of the experimental study. In total, 10,428 twenty-node reduced cubic elements (C3D20R) were used to mesh each CTS sample. The mesh sensitivity analysis was performed to obtain the optimum mesh size and the smallest element size around the crack tip was considered to be 0.1 mm.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFinally, the determined compliance values were plotted versus the crack length. Based on the MCC method [\u003cspan additionalcitationids=\"CR9\" citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e] and using the curve fitting method, a second-order polynomial equation was obtained for each compliance-crack length curve:\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$C={\\gamma a}^{2}+\\delta a+{\\lambda }$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cem\u003eγ\u003c/em\u003e, \u003cem\u003eδ\u003c/em\u003e and \u003cem\u003eλ\u003c/em\u003e can be computed according to the curve fitting process. In addition, \u003cem\u003ea\u003c/em\u003e is the crack length of the CTS sample. The translaminar CSERR of a laminated composites system under a specific loading condition can be computed by the following equation [\u003cspan additionalcitationids=\"CR9\" citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]:\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$${G}_{c}=\\frac{{P}_{c}^{2}}{2t}\\frac{dC}{da}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cem\u003eC\u003c/em\u003e, \u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u003c/sub\u003e, and \u003cem\u003et\u003c/em\u003e are the compliance, the critical load, and the thickness of CTS sample. At the end, substituting Eq.\u0026nbsp;(\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e) into Eq.\u0026nbsp;(\u003cspan refid=\"Equ2\" class=\"InternalRef\"\u003e2\u003c/span\u003e), the translaminar CSERR of a laminated composites system can be determined as follows:\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$${G}_{c}={\\left.\\frac{{P}_{c}^{2}}{2t}(2\\gamma a+\\delta )\\right|}_{a={a}_{0}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cem\u003ea\u003c/em\u003e\u003csub\u003e\u003cem\u003e0\u003c/em\u003e\u003c/sub\u003e is the summation of the pre-crack and notch lengths. Figure\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e shows the compliance-crack length plots obtained from the finite element analysis for the cotton/epoxy samples under different loadings.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe translaminar CSERR components of the CTS specimen under any mixed mode I/II loading condition can be computed as follows:\u003cdiv id=\"Equ4\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ4\" name=\"EquationSource\"\u003e\n$${G}_{I}={\\left.\\frac{{\\left({P}_{c}Cos\\alpha \\right)}^{2}}{2t}(2\\gamma a+\\delta )\\right|}_{a={a}_{0}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ5\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ5\" name=\"EquationSource\"\u003e\n$${G}_{II}={\\left.\\frac{{\\left({P}_{c}Sin\\alpha \\right)}^{2}}{2t}(2\\gamma a+\\delta )\\right|}_{a={a}_{0}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e5\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\alpha\\)\u003c/span\u003e\u003c/span\u003e is the loading angle as shown in Figs.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e and \u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. It must be noted that \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\alpha =0\\)\u003c/span\u003e\u003c/span\u003e and 90\u0026ordm; denote the pure mode I and II loading conditions, respectively. In addition, under mixed mode I/II loading state, the total CSERR can be obtained as:\u003cdiv id=\"Equ6\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ6\" name=\"EquationSource\"\u003e\n$${G}_{c}={G}_{I}+{G}_{II}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e6\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eFor the laminated composite materials under mode I and II loading states, the translaminar stress intensity factor can be written as a function of the strain energy release rate as follows [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]:\u003cdiv id=\"Equ7\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ7\" name=\"EquationSource\"\u003e\n$${K}_{I}=\\sqrt{{G}_{I}{E}_{I}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e7\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ8\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ8\" name=\"EquationSource\"\u003e\n$${K}_{II}=\\sqrt{{G}_{II}{E}_{II}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e8\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eIn the above relations, \u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003eI\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003eII\u003c/em\u003e\u003c/sub\u003e denote the effective tensile moduli of the laminated composites under a plane stress condition and can be determined by the following relations [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]:\u003cdiv id=\"Equ9\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ9\" name=\"EquationSource\"\u003e\n$${E}_{I}=\\sqrt{2/\\left({a}_{11}{a}_{22}\\right)}/\\sqrt{\\sqrt{{a}_{22}/{a}_{11}}+\\left\\{\\left({2a}_{12}+{a}_{66}\\right)/\\left({2a}_{11}\\right)\\right\\}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e9\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ10\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ10\" name=\"EquationSource\"\u003e\n$${E}_{II}=\\left(\\sqrt{2}/{a}_{11}\\right)/\\sqrt{\\sqrt{{a}_{22}/{a}_{11}}+\\left\\{\\left({2a}_{12}+{a}_{66}\\right)/\\left({2a}_{11}\\right)\\right\\}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e10\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cem\u003ea\u003c/em\u003e\u003csub\u003eij\u003c/sub\u003e are written as functions of the engineering elastic terms of the laminated composites [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]:\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Tabb\" border=\"1\"\u003e \u003ccolgroup cols=\"7\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({a}_{11}=\\frac{1}{{E}_{xx}}\\)\u003c/span\u003e\u003c/span\u003e,\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({a}_{22}=\\frac{1}{{E}_{yy}}\\)\u003c/span\u003e\u003c/span\u003e,\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({a}_{33}=\\frac{1}{{E}_{zz}}\\)\u003c/span\u003e\u003c/span\u003e,\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({a}_{44}=\\frac{1}{{G}_{yz}}\\)\u003c/span\u003e\u003c/span\u003e,\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({a}_{55}=\\frac{1}{{G}_{xz}}\\)\u003c/span\u003e\u003c/span\u003e,\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c7\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e(11)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({a}_{66}=\\frac{1}{{G}_{xy}}\\)\u003c/span\u003e\u003c/span\u003e,\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({a}_{12}={a}_{21}=-\\frac{{\\upsilon }_{xy}}{{E}_{xx}}=-\\frac{{\\upsilon }_{yx}}{{E}_{yy}}\\)\u003c/span\u003e\u003c/span\u003e,\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"3\" nameend=\"c6\" namest=\"c4\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({a}_{13}={a}_{31}=-\\frac{{\\upsilon }_{xz}}{{E}_{xx}}=-\\frac{{\\upsilon }_{zx}}{{E}_{zz}}\\)\u003c/span\u003e\u003c/span\u003e,\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({a}_{23}={a}_{32}=-\\frac{{\\upsilon }_{yz}}{{E}_{yy}}=-\\frac{{\\upsilon }_{zy}}{{E}_{zz}}\\)\u003c/span\u003e\u003c/span\u003e,\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"7\"\u003eIn addition, the TFT of the laminate specimens subjected to any mixed mode loading state can be determined as follows:\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003cdiv id=\"Equ11\" class=\"Equation\"\u003e \u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ11\" name=\"EquationSource\"\u003e\n$${K}_{c}=\\sqrt{{K}_{I}^{2}+{K}_{II}^{2}}$$\u003c/div\u003e \u003cdiv class=\"EquationNumber\"\u003e12\u003c/div\u003e\u003c/div\u003e \u003c/p\u003e"},{"header":"5. Results and discussion","content":"\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003e5.1. Load-displacement curves\u003c/h2\u003e \u003cp\u003eTypical load-displacement curves were obtained from the translaminar fracture testing of the cotton/epoxy samples under different temperature values and loading conditions. Figure\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003ea shows the effect of mode mixity on the behavior of cotton/epoxy composites at 30 ˚C. As demonstrated, the area under the load-displacement curve is increased by enhancing the contribution of mode II loading condition. Figures\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003eb and c display the response of the cotton/epoxy laminated composites having a translaminar crack under different loading conditions tested at 0 and \u0026minus;\u0026thinsp;30 ˚C, respectively.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigures\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003ea-d demonstrate the influence of temperature on the load-displacement curves of translaminar fracture of cotton/epoxy samples under different loading states. As observed, the translaminar fracture behavior of the cotton/epoxy laminated composites is strongly influenced by temperature. It is well observed that under any loading condition, by decreasing the temperature, the maximum load and the maximum deflection of the cotton/epoxy sample is reduced significantly. Besides, when the cotton/epoxy laminated composites is placed at room temperature, the load-displacement of the CTS sample has a linear elastic behavior till the maximum load and then the load is reduced suddenly. However, by lowering the temperature from 30 to 0 \u0026ordm;C, in in addition to linear response, a non-linear behavior is observed in the load-displacement curve before the maximum load. For the samples placed at -30 \u0026ordm;C, a major non-linear behavior was observed before the maximum load. Besides, unlike the other curves, after the maximum load, the curve not only does not suddenly decrease but also slightly degrades.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThree values for CSERR of a laminated composites system at the crack growth initiation state, i.e., onset of nonlinearity (NL), visual observation (VIS), and maximum load (MAX), have been introduced in the literature [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e, \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e]. These values correspond to three values of load in the load-displacement curve of each fracture sample, i.e., P\u003csub\u003eNL\u003c/sub\u003e, P\u003csub\u003eVIS\u003c/sub\u003e, and P\u003csub\u003eMAX\u003c/sub\u003e. Some investigators [\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e, \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e] have expressed that the crack growth initiation occurs when P\u003csub\u003eNL\u003c/sub\u003e. The others have believed that the crack growth initiation in the laminated composites happens at P\u0026thinsp;=\u0026thinsp;P\u003csub\u003eMAX\u003c/sub\u003e [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e, \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e, \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e]. Among the three CSERR initiation values, the NL CSERR (\u003cem\u003eG\u003c/em\u003e\u003csub\u003e\u003cem\u003eC\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e-\u003c/em\u003e\u003csub\u003e\u003cem\u003eNL\u003c/em\u003e\u003c/sub\u003e) typically has the lowest value. Besides, according to ASTM E1922 [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e], the upper bound value of the CSERR can be computed using the maximum load. Hence, in current research, the onset of nonlinearity load points were employed to compute the translaminar CSERR of the laminated composites under different loading and temperature conditions. In Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, the values of critical load for cotton/epoxy samples exposed to different temperatures have been summarized. As mentioned, the samples were tested under pure mode I, pure mode II and mixed mode I/II loadings. The critical load is required to calculate the CSERR according to Eq.\u0026nbsp;(\u003cspan refid=\"Equ3\" class=\"InternalRef\"\u003e3\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eThe critical load (N) values obtained for the cotton/epoxy laminated composites under different temperature and loading conditions\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eLoading condition\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"3\" nameend=\"c4\" namest=\"c2\"\u003e \u003cp\u003eTemperature (˚C)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-30\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003ePure Mode I (α\u0026thinsp;=\u0026thinsp;0\u0026ordm;)\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1131.8\u0026thinsp;\u0026plusmn;\u0026thinsp;45.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e496.3\u0026thinsp;\u0026plusmn;\u0026thinsp;18.9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e150.3\u0026thinsp;\u0026plusmn;\u0026thinsp;12.5\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eMixed mode I/II (α\u0026thinsp;=\u0026thinsp;30\u0026ordm;)\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1125.3\u0026thinsp;\u0026plusmn;\u0026thinsp;37.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e816.9\u0026thinsp;\u0026plusmn;\u0026thinsp;25.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e231.0\u0026thinsp;\u0026plusmn;\u0026thinsp;10.7\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eMixed mode I/II (α\u0026thinsp;=\u0026thinsp;60\u0026ordm;)\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1270.4\u0026thinsp;\u0026plusmn;\u0026thinsp;36.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e858.2\u0026thinsp;\u0026plusmn;\u0026thinsp;23.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e297.9\u0026thinsp;\u0026plusmn;\u0026thinsp;16.6\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003ePure Mode II (α\u0026thinsp;=\u0026thinsp;90\u0026ordm;)\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1789.0\u0026thinsp;\u0026plusmn;\u0026thinsp;65.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1030.5\u0026thinsp;\u0026plusmn;\u0026thinsp;38.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e450.6\u0026thinsp;\u0026plusmn;\u0026thinsp;19.2\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003e5.2. CSERR calculation\u003c/h2\u003e \u003cp\u003eThe values of translaminar CSERR corresponded to the critical load (\u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003eNL\u003c/em\u003e\u003c/sub\u003e) was determined using Eq.\u0026nbsp;(\u003cspan refid=\"Equ3\" class=\"InternalRef\"\u003e3\u003c/span\u003e). According to the plots displayed in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e, the translaminar critical strain energy release rate of cotton/epoxy samples under different temperature and loading conditions have been listed in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. As observed, by increasing the mode II loading contribution, the value of the translaminar CSERR increases. In other words, the lowest and highest values of the translaminar CSERR are obtained when the samples are tested under the pure modes I and II, respectively. In addition, as the temperature decreases, the values of the CSERR degrade significantly. The biggest reduction was also calculated for the sample tested under the mode I loading state. Gonzalez et al. [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e] observed that the translaminar fracture toughness of a thermoplastic laminated composites is increased slightly subjected to the tensile loading with the change of temperature from 0 to 150 \u0026ordm;C, while under compressive loading, the temperature has a strong effect on the translaminar fracture toughness.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eThe translaminar critical strain energy release rate (kJ/m\u003csup\u003e2\u003c/sup\u003e) of the cotton/epoxy laminated composites under different temperature values and loading conditions\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eLoading condition\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"3\" nameend=\"c4\" namest=\"c2\"\u003e \u003cp\u003eTemperature (˚C)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-30\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003ePure Mode I (α\u0026thinsp;=\u0026thinsp;0\u0026ordm;)\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e10.37\u0026thinsp;\u0026plusmn;\u0026thinsp;0.85\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.99\u0026thinsp;\u0026plusmn;\u0026thinsp;0.15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.19\u0026thinsp;\u0026plusmn;\u0026thinsp;0.03\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eMixed mode I/II (α\u0026thinsp;=\u0026thinsp;30\u0026ordm;)\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e11.76\u0026thinsp;\u0026plusmn;\u0026thinsp;0.80\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e6.19\u0026thinsp;\u0026plusmn;\u0026thinsp;0.39\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.49\u0026thinsp;\u0026plusmn;\u0026thinsp;0.05\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eMixed mode I/II (α\u0026thinsp;=\u0026thinsp;60\u0026ordm;)\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e11.92\u0026thinsp;\u0026plusmn;\u0026thinsp;0.69\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e5.44\u0026thinsp;\u0026plusmn;\u0026thinsp;0.30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.66\u0026thinsp;\u0026plusmn;\u0026thinsp;0.08\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003ePure Mode II (α\u0026thinsp;=\u0026thinsp;90\u0026ordm;)\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e12.32\u0026thinsp;\u0026plusmn;\u0026thinsp;0.92\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e4.09\u0026thinsp;\u0026plusmn;\u0026thinsp;0.31\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.78\u0026thinsp;\u0026plusmn;\u0026thinsp;0.07\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003e5.3. Fracture envelops\u003c/h2\u003e \u003cp\u003eIn literature, different criteria have been proposed to investigate the response of the laminated composites system under mixed mode I/II loading conditions. Mixed Mode Fracture Envelope (MMFE) is extensively employed to evaluate the fracture testing of laminated composites [\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e]. In this study, a modified MMFE is proposed to estimate the mixed mode I/II translaminar behavior of the cotton/epoxy laminated composites at different temperatures. This criterion is expressed by the following relation:\u003cdiv id=\"Equ12\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ12\" name=\"EquationSource\"\u003e\n$$\\frac{{(\\frac{{K}_{I}}{{K}_{IC}}-m)}^{2}}{{X}^{2}}+\\frac{{(\\frac{{K}_{II}}{{K}_{IIC}}-n)}^{2}}{{Y}^{2}}=1$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e13\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eFigures\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003ea-b show the mixed mode I/II translaminar fracture envelope for the cotton/epoxy laminated composites at 30, 0, and \u0026minus;\u0026thinsp;30 \u0026ordm;C. It was concluded that the form of \u003cem\u003em\u003c/em\u003e\u0026thinsp;=\u0026thinsp;\u003cem\u003en\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0 and X\u0026thinsp;=\u0026thinsp;Y\u0026thinsp;=\u0026thinsp;1 is properly predicted the translaminar fracture response of the cotton/epoxy laminated composites at 30 \u0026ordm;C (see Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003ea). These fitted Modified MMFE relations for the system at 0 and \u0026minus;\u0026thinsp;30 \u0026ordm;C have also been shown in Figs.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003eb-c. As observed, the modified MMFE is able to predict the mixed mode I/II translaminar fracture response of the cotton/epoxy laminated composites at different temperature conditions.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"6. Conclusions","content":"\u003cp\u003eIn the present research, the effect of temperatures on the translaminar fracture properties of the cotton/epoxy laminated composites under pure mode I, pure mode II and mixed mode I/II loading conditions was investigated. Some achievements of this research have been summarized as follows:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eTemperature greatly affects the translaminar fracture properties of cotton/epoxy composites.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eThe results showed that temperature has the greatest effect on the mode I CSERR. As the temperature decreased from 30 to 0\u0026deg;C, the translaminar CSERR under mode I loading condition degraded by 80%. In addition, the temperature decreased from 0 to -30\u0026deg;C, the mode I translaminar CSERR decreased around 90%.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eAmong the different loading states, the mode II had the least dependence on the temperature. As the temperature decreased from 30 to 0\u0026deg;C, the value of the mode II translaminar CSERR decreased by 66%.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eBy changing the loading condition from the mode I to the mixed mode I/II as well as the mode II, the amount of translaminar CSERR decreased. In other words, with the enhancement of the contribution of the mode II loading condition, the value of the translaminar CSERR increased.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eA modified version of Mixed Mode Fracture Envelope criterion was proposed to predict the translaminar fracture response of the cotton/epoxy laminated composites placed at different temperature values under mixed mode I/II loading conditions.\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e"},{"header":"Nomenclature","content":"\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\" width=\"638\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd width=\"11.755485893416928%\" rowspan=\"2\" valign=\"top\"\u003e\n \u003cp\u003e\u003cem\u003ea\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"30.564263322884013%\" rowspan=\"2\" valign=\"top\"\u003e\n \u003cp\u003eSummation of pre-crack and notch lengths\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"15.987460815047022%\" valign=\"top\"\u003e\n \u003cp\u003e\u003cem\u003en\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"41.692789968652036%\" valign=\"top\"\u003e\n \u003cp\u003eFracture envelop parameter\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"27.717391304347824%\" valign=\"top\"\u003e\n \u003cp\u003e\u003cem\u003eP\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"72.28260869565217%\" valign=\"top\"\u003e\n \u003cp\u003eApplied load\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"11.755485893416928%\" valign=\"top\"\u003e\n \u003cp\u003e\u003cem\u003ea\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"30.564263322884013%\" valign=\"top\"\u003e\n \u003cp\u003eNotch length\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"15.987460815047022%\" valign=\"top\"\u003e\n \u003cp\u003e\u003cem\u003eP\u003csub\u003eC\u003c/sub\u003e\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"41.692789968652036%\" valign=\"top\"\u003e\n \u003cp\u003eCritical applied load\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"11.755485893416928%\" valign=\"top\"\u003e\n \u003cp\u003e\u003cem\u003eC\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"30.564263322884013%\" valign=\"top\"\u003e\n \u003cp\u003eCompliance\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"15.987460815047022%\" valign=\"top\"\u003e\n \u003cp\u003e\u003cem\u003eW\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"41.692789968652036%\" valign=\"top\"\u003e\n \u003cp\u003eCTS sample width\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"11.755485893416928%\" valign=\"top\"\u003e\n \u003cp\u003e\u003cem\u003eE\u003csub\u003eI\u003c/sub\u003e\u0026nbsp;\u003c/em\u003e\u0026amp;\u003cem\u003e\u0026nbsp;E\u003csub\u003eII\u003c/sub\u003e\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"30.564263322884013%\" valign=\"top\"\u003e\n \u003cp\u003eEffective tensile stiffnesses\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"15.987460815047022%\" valign=\"top\"\u003e\n \u003cp\u003e\u003cem\u003et\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"41.692789968652036%\" valign=\"top\"\u003e\n \u003cp\u003eCTS sample thickness\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"11.755485893416928%\" valign=\"top\"\u003e\n \u003cp\u003e\u003cem\u003eE\u003csub\u003exx\u003c/sub\u003e\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"30.564263322884013%\" valign=\"top\"\u003e\n \u003cp\u003eLongitudinal tensile stiffness\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"15.987460815047022%\" valign=\"top\"\u003e\n \u003cp\u003e\u003cem\u003eX\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"41.692789968652036%\" valign=\"top\"\u003e\n \u003cp\u003eFracture envelop parameter\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"11.755485893416928%\" valign=\"top\"\u003e\n \u003cp\u003e\u003cem\u003eE\u003csub\u003eyy\u003c/sub\u003e\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"30.564263322884013%\" valign=\"top\"\u003e\n \u003cp\u003eTransverse tensile stiffness\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"15.987460815047022%\" valign=\"top\"\u003e\n \u003cp\u003e\u003cem\u003eY\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"41.692789968652036%\" valign=\"top\"\u003e\n \u003cp\u003eFracture envelop parameter\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"11.755485893416928%\" valign=\"top\"\u003e\n \u003cp\u003e\u003cem\u003eE\u003csub\u003es\u003c/sub\u003e\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"30.564263322884013%\" valign=\"top\"\u003e\n \u003cp\u003eIn-plane shear stiffness\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"15.987460815047022%\" valign=\"top\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003eAbbreviations\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"41.692789968652036%\" valign=\"top\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"11.755485893416928%\" valign=\"top\"\u003e\n \u003cp\u003e\u003cem\u003eG\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"30.564263322884013%\" valign=\"top\"\u003e\n \u003cp\u003eStrain energy release rate\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"15.987460815047022%\" valign=\"top\"\u003e\n \u003cp\u003eASTM\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"41.692789968652036%\" valign=\"top\"\u003e\n \u003cp\u003eAmerican Society for Testing and Materials\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"11.755485893416928%\" rowspan=\"2\" valign=\"top\"\u003e\n \u003cp\u003e\u003cem\u003eG\u003csub\u003ec\u003c/sub\u003e\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"30.564263322884013%\" rowspan=\"2\" valign=\"top\"\u003e\n \u003cp\u003eCritical strain energy release\u003c/p\u003e\n \u003cp\u003erate (CSERR)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"15.987460815047022%\" valign=\"top\"\u003e\n \u003cp\u003eC3D20R\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"41.692789968652036%\" valign=\"top\"\u003e\n \u003cp\u003eReduced twenty-node quadratic elements\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"27.717391304347824%\" valign=\"top\"\u003e\n \u003cp\u003eCSERR\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"72.28260869565217%\" valign=\"top\"\u003e\n \u003cp\u003ecritical strain energy release rate\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"11.755485893416928%\" valign=\"top\"\u003e\n \u003cp\u003e\u003cem\u003eG\u003csub\u003eIc\u003c/sub\u003e\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"30.564263322884013%\" valign=\"top\"\u003e\n \u003cp\u003eMode I CSERR\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"15.987460815047022%\" valign=\"top\"\u003e\n \u003cp\u003eCT\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"41.692789968652036%\" valign=\"top\"\u003e\n \u003cp\u003eCompact Tension\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"11.755485893416928%\" valign=\"top\"\u003e\n \u003cp\u003e\u003cem\u003eG\u003csub\u003eIIc\u003c/sub\u003e\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"30.564263322884013%\" valign=\"top\"\u003e\n \u003cp\u003eMode II\u0026nbsp;CSERR\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"15.987460815047022%\" valign=\"top\"\u003e\n \u003cp\u003eCTS\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"41.692789968652036%\" valign=\"top\"\u003e\n \u003cp\u003eCompact Tension Shear\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"11.755485893416928%\" valign=\"top\"\u003e\n \u003cp\u003e\u003cem\u003eG\u003csub\u003eI-IIc\u003c/sub\u003e\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"30.564263322884013%\" valign=\"top\"\u003e\n \u003cp\u003eMixed mode I/II CSERR\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"15.987460815047022%\" valign=\"top\"\u003e\n \u003cp\u003eFEM\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"41.692789968652036%\" valign=\"top\"\u003e\n \u003cp\u003eFinite Element method\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"11.755485893416928%\" valign=\"top\"\u003e\n \u003cp\u003e\u003cem\u003eH\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"30.564263322884013%\" valign=\"top\"\u003e\n \u003cp\u003eCTS sample height\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"15.987460815047022%\" valign=\"top\"\u003e\n \u003cp\u003eMCC\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"41.692789968652036%\" valign=\"top\"\u003e\n \u003cp\u003eModified\u0026nbsp;Compliance Calibration\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"11.755485893416928%\" rowspan=\"2\" valign=\"top\"\u003e\n \u003cp\u003e\u003cem\u003eK\u003csub\u003eI\u003c/sub\u003e\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"30.564263322884013%\" rowspan=\"2\" valign=\"top\"\u003e\n \u003cp\u003eMode I stress intensity factor (SIF)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"15.987460815047022%\" valign=\"top\"\u003e\n \u003cp\u003eNL\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"41.692789968652036%\" valign=\"top\"\u003e\n \u003cp\u003eOnset of non-linearity\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"27.717391304347824%\" valign=\"top\"\u003e\n \u003cp\u003eTFT\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"72.28260869565217%\" valign=\"top\"\u003e\n \u003cp\u003eTranslaminar Fracture Toughness\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"11.755485893416928%\" valign=\"top\"\u003e\n \u003cp\u003e\u003cem\u003eK\u003csub\u003eII\u003c/sub\u003e\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"30.564263322884013%\" valign=\"top\"\u003e\n \u003cp\u003eMode II SIF\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"15.987460815047022%\" valign=\"top\"\u003e\n \u003cp\u003eVIS\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"41.692789968652036%\" valign=\"top\"\u003e\n \u003cp\u003eVisual observation\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"11.755485893416928%\" rowspan=\"2\" valign=\"top\"\u003e\n \u003cp\u003e\u003cem\u003eK\u003csub\u003eIc\u003c/sub\u003e\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"30.564263322884013%\" rowspan=\"2\" valign=\"top\"\u003e\n \u003cp\u003eMode I translaminar fracture toughness (TFT)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"15.987460815047022%\" valign=\"top\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"41.692789968652036%\" valign=\"top\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"27.717391304347824%\" valign=\"top\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003eGreek letters\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"72.28260869565217%\" valign=\"top\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"11.755485893416928%\" valign=\"top\"\u003e\n \u003cp\u003e\u003cem\u003eK\u003csub\u003eIIc\u003c/sub\u003e\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"30.564263322884013%\" valign=\"top\"\u003e\n \u003cp\u003eMode II TFT\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"15.987460815047022%\" valign=\"top\"\u003e\n \u003cp\u003e\u0026alpha;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"41.692789968652036%\" valign=\"top\"\u003e\n \u003cp\u003eIn-plane loading angle\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"11.755485893416928%\" valign=\"top\"\u003e\n \u003cp\u003e\u003cem\u003eK\u003csub\u003eI-IIc\u003c/sub\u003e\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"30.564263322884013%\" valign=\"top\"\u003e\n \u003cp\u003eMixed mode I/II TFT\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"15.987460815047022%\" valign=\"top\"\u003e\n \u003cp\u003e\u003cem\u003ev\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"41.692789968652036%\" valign=\"top\"\u003e\n \u003cp\u003ePoisson\u0026rsquo;s ratio\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"11.755485893416928%\" valign=\"top\"\u003e\n \u003cp\u003e\u003cem\u003eK\u003csub\u003eT\u003c/sub\u003e\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"30.564263322884013%\" valign=\"top\"\u003e\n \u003cp\u003eTotal SIF\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"15.987460815047022%\" valign=\"top\"\u003e\n \u003cp\u003e\u0026gamma;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"41.692789968652036%\" valign=\"top\"\u003e\n \u003cp\u003eCompliance fitting parameter\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"11.755485893416928%\" valign=\"top\"\u003e\n \u003cp\u003e\u003cem\u003em\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"30.564263322884013%\" valign=\"top\"\u003e\n \u003cp\u003eFracture envelop parameter\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"15.987460815047022%\" valign=\"top\"\u003e\n \u003cp\u003e\u003cem\u003e\u0026delta;\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"41.692789968652036%\" valign=\"top\"\u003e\n \u003cp\u003eCompliance fitting parameter\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e"},{"header":"Declarations","content":"\u003cp\u003e \u003cstrong\u003eEthical Approval\u003c/strong\u003e \u003cp\u003eThe authors certify that they have NO affiliations with or involvement in any organization or entity with any financial interest, or non-financial interest in the subject matter or materials discussed in this work.\u003c/p\u003e \u003c/p\u003e\u003ch2\u003eFunding\u003c/h2\u003e \u003cp\u003eThis research received no grant from any funding agency in the public, commercial, or the others.\u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eAfshin Zeinedini wrote the main manuscript, prepared the figures, and carried out the FE analysis. Yosra Basim Hassan performed the experimental study.\u003c/p\u003e\u003ch2\u003eAvailability of data and materials\u003c/h2\u003e \u003cp\u003eThe raw/processed data required to reproduce these findings cannot be shared at this time as the data also forms part of an ongoing study.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eZeinedini, A., Hosseini, Y., Mahdi, A.S. et al.: Impact of the Manufacturing Process on the Flexural Properties of Laminated Composite-Metal Riveted Joints: Experimental and Numerical Studies. Appl. Compos. Mater. 31 (2024) 583\u0026ndash;610. https://doi.org/10.1007/s10443-023-10186-w\u003c/li\u003e\n\u003cli\u003eCai, M., Liu, J., Zhang, X. et al.: Mechanical Stability of Carbon/Ramie Fiber Hybrid Composites Under Hygrothermal Aging. Appl Compos Mater (2024). https://doi.org/10.1007/s10443-024-10211-6\u003c/li\u003e\n\u003cli\u003eMoradi, E., Zeinedini, A.: On the Mixed Mode I/II/III Inter-laminar Fracture Toughness of Cotton/Epoxy Laminated Composites. Theor. Appl. Fract. Mech. (2019). https://doi.org/10.1016/j.tafmec.2019.102400\u003c/li\u003e\n\u003cli\u003eShokrieh, M.M., Zeinedini, A.: A Novel Method for Calculation of Strain Energy Release Rate of Asymmetric Double Cantilever Laminated Composite Beams. Appl Compos Mater (2014). https://doi.org/10.1007/s10443-013-9328-5\u003c/li\u003e\n\u003cli\u003eAhmadi, S., Zeinedini, A.: Experimental, theoretical and numerical investigation of the drilling effects on mode I delamination of laminated composites. Aerosp. Sci. Technol. (2020). https://doi.org/10.1016/j.ast.2020.105992\u003c/li\u003e\n\u003cli\u003eJahanian, E., Zeinedini, A.: Influence of drilling on mode II delamination of E-glass/epoxy laminated composites. Theor. Appl. Fract. Mech. (2018). https://doi.org/10.1016/j.tafmec.2018.06.002\u003c/li\u003e\n\u003cli\u003eZeinedini, A., Shokrieh, M.M., Ebrahimi, A.: The effect of agglomeration on the fracture toughness of CNTs-reinforced nanocomposites. Theor. Appl. Fract. Mech. (2018). https://doi.org/10.1016/j.tafmec.2018.01.009\u003c/li\u003e\n\u003cli\u003eTaghibeigi, H., Zeinedini, A., Oleiwi, A.H.: On the mixed mode I/II translaminar fracture of plain-weave carbon, E-glass and Kevlar reinforced laminated composites. Compos. Sci. Tech. (2023). https://doi.org/10.1016/j.compscitech.2023.110117\u003c/li\u003e\n\u003cli\u003eLaffan, M.J., Pinho, S.T., Robinson, P., McMillan, A.J.: Translaminar fracture toughness testing of composites: a review. Polym. Test. (2012). https://doi.org/10.1016/j.polymertesting.2012.01.002\u003c/li\u003e\n\u003cli\u003eZeinedini, A., Moradi, M.H., Taghibeigi, H., Jamali, J.: on the mixed mode I/II/III translaminar fracture thoughness of Cotton/epoxy laminated composites. Theor. Appl. Fract. Mech. (2020). https://doi.org/10.1016/j.tafmec.2020.102760\u003c/li\u003e\n\u003cli\u003eUnderwood, J.H., Kortschot, M.T.: Notch-tip Damage and Translaminar Fracture Toughness Measurements from Carbon/Epoxy Laminates. US Army Armament Research. Development and Engineering Centre, Technical Report ARCCB-TR-94010 (1994). \u003c/li\u003e\n\u003cli\u003eGigliotti, L., Pinho, S.T.: Translaminar fracture toughness of NCF composites with multiaxial blankets. Mater. Des. (2016). https://doi.org/10.1016/j.matdes.2015.12.167\u003c/li\u003e\n\u003cli\u003eGonzalez, J.D.P., Vieille, B., Bouvet, C.: High temperature translaminar fracture of Woven-ply thermoplastic laminates in tension and in compression. Eng. Fract. Mech. (2021). https://doi.org/10.1016/j.engfracmech.2021.107616\u003c/li\u003e\n\u003cli\u003eSaadati, Y., Lebrun, G., Bouvet, C., Chatelain, J.F.: Study of translaminar Fracture Thoughness of unidirectional Flax/epoxy composite. Compos. C: Open Access (2020). https://doi.org/10.1016/j.jcomc.2020.100008\u003c/li\u003e\n\u003cli\u003eHaldar, S\u003cspan dir=\"RTL\"\u003e.\u003c/span\u003e, Herraez, M., Naya, F., Gonzalez, C., Lopes, S.C.: Relations between interlaminar micromechanisms and translaminar fracture behavior of unidirectional FRP supported by experimental mocromechanics. Compos. B Eng. (2019). https://doi.org/10.1016/j.compositesb.2019.107000\u003c/li\u003e\n\u003cli\u003eSyed Abdullah, S.I.B., Iannucci L., Greenhalgh E.S.: On the translaminar fracture thoughness of vectran/epoxy composite material. Compos. Struct. (2018). https://doi.org/10.1016/j.compstruct.2018.03.004\u003c/li\u003e\n\u003cli\u003eDesai, A., Sharanaprabhu, C.M., Kudari, S.K.: Study on translaminar fracture Toughness under mixed mode I/II load for (0/45) orientation unidirectional glass/epoxy composite. Mater. Today Proc. 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(2020). https://doi.org/10.1177/0967391120982751\u003c/li\u003e\n\u003cli\u003eDoostvandi, B., Zeinedini, A.: Repair of inclined notches in the pressurized steel pipes using laminated composites, Material Design \u0026amp; Processing Communications, Mat Design Process Comm (2019). https://doi.org/10.1002/mdp2.49\u003c/li\u003e\n\u003cli\u003eShahmaleki, M., Zeinedini, A.: Flexural Properties of 3D-printed Hierarchical-Sinusoidal Corrugated Core Sandwich Panels with Natural Fiber Reinforced Skins. Polym. Polym. Compos. (2022). https://doi.org/10.1177/09673911221101299\u003c/li\u003e\n\u003cli\u003eDaliri, V., Zeinedini, A.: Flexural Behavoiur of the Composite Sandwich Panels with Novel and Regular Corrugated Cores. Appl Compos Mater (2019). https://doi.org/10.1007/s10443-019-09761-x\u003c/li\u003e\n\u003cli\u003ePiroozfar, S., Zeinedini, A.: Effect of Geometrical Parameters on the Flexural Properties of Sandwich Structures with 3D-printed Honeycomb Core and E-glass/epoxy Face-sheets. Struct. (2021). https://doi.org/10.1016/j.istruc.2021.06.033\u003c/li\u003e\n\u003cli\u003ePickering, K.L., Aruan Efendy, M.G., Le, T.M.: A review of recent developments in natural fibre composites and their mechanical performance. Compos. - A: Appl. Sci. Manuf. (2016). https://doi.org/10.1016/j.compositesa.2015.08.038\u003c/li\u003e\n\u003cli\u003eKarimah, A., Ridho, M.R., Munawar S.S., Adi D.S., Ismadi, Damayanti. R., Subiyanto, B., Fatriasari, W., Fudholi, A.: A review on natural fibers for development of eco-friendly bio-composite: characteristics, and utilizations. J. Mater. Res. Technol. (2021). https://doi.org/10.1016/j.jmrt.2021.06.014.\u003c/li\u003e\n\u003cli\u003eASTM D3039/D3039M-08.: Standard test method for tensile properties of polymer matrix composite materials. ASTM International, Philadelphia (2014).\u003c/li\u003e\n\u003cli\u003eASTM D3518/D3518M-18.: Standard Test Method for In-Plane Shear Response of Polymer Matrix Composite Materials by Tensile Test of a \u0026plusmn;45 Laminate. ASTM International, Philadelphia (2018).\u003c/li\u003e\n\u003cli\u003eASTM E1922.: Standard Test Method for Translaminar Fracture Toughness of Laminated and Pultruded Polymer Matrix Composite Materials. ASTM International, Philadelphia (2015).\u003c/li\u003e\n\u003cli\u003eTeixeira, R.F., Pinho, S.T., Robinson, P.: Thickness-dependence of the translaminar fracture toughness: experimental study using thin-ply composites. Compos. Part A Appl. Sci. Manuf. (2016). https://doi.org/10.1016/j.compositesa.2016.05.031\u003c/li\u003e\n\u003cli\u003eZeinedini, A.: A novel fixture for mixed mode I/II/III fracture testing of brittle materials. Fatigue Fract Eng Mater Struct. (2018). https://doi.org/10.1111/ffe.12955\u003c/li\u003e\n\u003cli\u003eSwolfs, Y., Geboes, Y., Gorbatikh, L., Pinho, S.T.: The importance of translaminar fracture toughness for the penetration impact behavior of woven carbon/glass hybrid composites. Compos. Appl. Sci. Manuf. (2017). https://doi.org/10.1016/j.compositesa.2017.09.009\u003c/li\u003e\n\u003cli\u003eASTM D5528.: Standard Test Method for Mode I Interlaminar Fracture Toughness of Unidirectional Fiber-Reinforced Polymer Matrix Composites. ASTM International, Philadelphia (2013).\u003c/li\u003e\n\u003cli\u003eEl-Sagheer, I., Abd-Elhady, A.A., Sallam, H.M., Naga, S.A.R.: An Assessment of ASTM E1922 for Measuring the Translaminar Fracture Toughness of Laminated Polymer Matrix Composite Materials. Polymers (2021). https://doi.org/10.3390/polym13183129\u003c/li\u003e\n\u003cli\u003eOzdemir, A.O., Karata, C.: Experimental determination of fracture toughness of woven/chopped glass fiber hybrid reinforced thermoplastic composite laminates. Sci. Iran. B (2021). https://doi.org/10.24200/SCI.2020.56380.4701\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"applied-composite-materials","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"acma","sideBox":"Learn more about [Applied Composite Materials](http://link.springer.com/journal/10443)","snPcode":"10443","submissionUrl":"https://submission.nature.com/new-submission/10443/3","title":"Applied Composite Materials","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Epoxy, fracture toughness, natural fiber, laminated composites, temperature, translaminar fracture","lastPublishedDoi":"10.21203/rs.3.rs-4193231/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4193231/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIn recent years, laminated composites reinforced with natural fibers have extensively used in the various industries. One of the most important failure modes of laminated composite materials is translaminar fracture under different loading conditions. In this research, the effect of temperature on the translaminar critical strain energy release rate (CSERR) of the composites reinforced with cotton fibers was investigated. The cotton/epoxy samples were placed at different temperature conditions of 30, 0, and \u0026minus;\u0026thinsp;30\u0026deg;C. The translaminar CSERR values of cotton/epoxy laminated composites were obtained under pure mode I, mixed mode I/II with two different loading angles, and pure mode II loading conditions. To calculate the translaminar CSERR based on experimental results, numerical modeling was also performed. Besides, a modified version of Mixed Mode Fracture Envelope criterion was proposed to predict the mixed mode I/II translaminar fracture behavior of the cotton/epoxy laminated composites at the mentioned temperatures. The results showed that lowering the temperature has a great impact on the translaminar CSERR. It was also concluded that the change in the temperature had the greatest effect on the value of the mode I translaminar CSERR. Moreover, as the temperature decreased from 30 to 0 and \u0026minus;\u0026thinsp;30\u0026deg;C, the value of the mode I translaminar CSERR decreased around 80 and 90%, respectively.\u003c/p\u003e","manuscriptTitle":"Effect of temperature on the mixed mode I/II translaminar fracture of laminated composites reinforced with natural fibers","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-04-04 16:01:15","doi":"10.21203/rs.3.rs-4193231/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2024-05-30T12:31:47+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-05-30T05:30:43+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"85574293480458847475201290650677904733","date":"2024-05-09T13:54:51+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-04-16T12:53:43+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"1005c10f-73e5-4667-b619-a6b33082cf18","date":"2024-04-12T00:03:26+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2024-04-09T19:39:44+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2024-04-03T07:24:02+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2024-04-01T04:59:31+00:00","index":"","fulltext":""},{"type":"submitted","content":"Applied Composite Materials","date":"2024-03-30T18:09:22+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"applied-composite-materials","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"acma","sideBox":"Learn more about [Applied Composite Materials](http://link.springer.com/journal/10443)","snPcode":"10443","submissionUrl":"https://submission.nature.com/new-submission/10443/3","title":"Applied Composite Materials","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"622badce-b6fb-4ff1-af45-d00ecb8a643c","owner":[],"postedDate":"April 4th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2024-09-16T16:01:47+00:00","versionOfRecord":{"articleIdentity":"rs-4193231","link":"https://doi.org/10.1007/s10443-024-10267-4","journal":{"identity":"applied-composite-materials","isVorOnly":false,"title":"Applied Composite Materials"},"publishedOn":"2024-09-14 15:57:28","publishedOnDateReadable":"September 14th, 2024"},"versionCreatedAt":"2024-04-04 16:01:15","video":"","vorDoi":"10.1007/s10443-024-10267-4","vorDoiUrl":"https://doi.org/10.1007/s10443-024-10267-4","workflowStages":[]},"version":"v1","identity":"rs-4193231","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4193231","identity":"rs-4193231","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}